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Positive-entropy geodesic flows on nilmanifolds
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Butler, Leo T. and Gelfreich, Vassili (2008) Positive-entropy geodesic flows on nilmanifolds. Nonlinearity, Volume 21 (Number 7). pp. 1423-1434. doi:10.1088/0951-7715/21/7/002 ISSN 0951-7715.
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Official URL: http://dx.doi.org/10.1088/0951-7715/21/7/002
Abstract
Let T-n be the nilpotent group of real n x n upper-triangular matrices with 1s on the diagonal. The Hamiltonian flow of a left-invariant Hamiltonian on T*T-n naturally reduces to the Euler flow on t(n)*, the dual of t(n) = Lie(T-n). This paper shows that the Euler flows of the standard Riemannian and sub-Riemannian structures of T-4 have transverse homoclinic points on all regular coadjoint orbits. As a corollary, left-invariant Riemannian metrics with positive topological entropy are constructed on all quotients D\T-n where D is a discrete subgroup of T-n and n >= 4.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Entropy, Differentiable manifolds, Geodesic flows | ||||
Journal or Publication Title: | Nonlinearity | ||||
Publisher: | Institute of Physics Publishing Ltd. | ||||
ISSN: | 0951-7715 | ||||
Official Date: | July 2008 | ||||
Dates: |
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Volume: | Volume 21 | ||||
Number: | Number 7 | ||||
Number of Pages: | 12 | ||||
Page Range: | pp. 1423-1434 | ||||
DOI: | 10.1088/0951-7715/21/7/002 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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